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Entropic risk (ERisk) is an established risk measure in finance, quantifying risk by an exponential re-weighting of rewards. We study ERisk for the first time in the context of turn-based stochastic games with the total reward objective.…
We develop horizon-aware anytime-valid tests and confidence sequences for bounded means under a strict deadline $N$. Using the betting/e-process framework, we cast horizon-aware betting as a finite-horizon optimal control problem with state…
In this article we consider the surplus process of an insurance company within the Cramer-Lundberg framework. We study the optimal reinsurance strategy and dividend distribution of an insurance company under proportional reinsurance, in…
Structuring a viable pension plan is a problem that arises in the study of financial contracts pricing and bears special importance these days. Deterministic pension models often rely on projections that are based on several assumptions…
We study in detail and explicitly solve the version of Kyle's model introduced in a specific case in \cite{BB}, where the trading horizon is given by an exponentially distributed random time. The first part of the paper is devoted to the…
Existence of stochastic financial equilibria giving rise to semimartingale asset prices is established under a general class of assumptions. These equilibria are expressed in real terms and span complete markets or markets with withdrawal…
In this paper, we study the behavior of the Hedge algorithm in the online stochastic setting. We prove that anytime Hedge with decreasing learning rate, which is one of the simplest algorithm for the problem of prediction with expert…
In an efficient stock market, the log-returns and their time-dependent variances are often jointly modelled by stochastic volatility models (SVMs). Many SVMs assume that errors in log-return and latent volatility process are uncorrelated,…
The proposed model modifies option pricing formulas for the basic case of log-normal probability distribution providing correspondence to formulated criteria of efficiency and completeness. The model is self-calibrating by historic…
Being able to predict the occurrence of extreme returns is important in financial risk management. Using the distribution of recurrence intervals---the waiting time between consecutive extremes---we show that these extreme returns are…
What would you do if you were invited to play a game where you were given \$25 and allowed to place bets for 30 minutes on a coin that you were told was biased to come up heads 60% of the time? This is exactly what we did, gathering 61…
Although there is a wide use of technical trading rules in stock markets, the profitability of them still remains controversial. This paper first presents and proves the upper bound of cumulative return, and then introduces many of…
Building on similarities between earthquakes and extreme financial events, we use a self-organized criticality-generating model to study herding and avalanche dynamics in financial markets. We consider a community of interacting investors,…
We used the random walk to model the problem of reserves. The classic case of a stochastic process is the example of random walks, which are used to study a set of phenomena and, particularly, as in this article, models of reserves…
The gambler's ruin problem for correlated random walks (CRW), both with and without delays, is addressed using the Optional Stopping Theorem for martingales. We derive closed-form expressions for the ruin probabilities and the expected game…
This paper introduces a novel stochastic control framework to enhance the capabilities of automated investment managers, or robo-advisors, by accurately inferring clients' investment preferences from past activities. Our approach leverages…
We investigate the general problem of how to model the kinematics of stock prices without considering the dynamical causes of motion. We propose a stochastic process with long-range correlated absolute returns. We find that the model is…
Harrel's concordance index is a commonly used discrimination metric for survival models, particularly for models where the relative ordering of the risk of individuals is time-independent, such as the proportional hazards model. There are…
Fluctuations of observables as functions of time, or "fluctuation patterns", are studied in a chaotic microscopically reversible system that has irreversibly reached a nonequilibrium stationary state. Supposing that during a certain, long…
We present a simple dynamical model of stock index returns which is grounded on the ability of the Cyclically Adjusted Price Earning (CAPE) valuation ratio devised by Robert Shiller to predict long-horizon performances of the market. More…